Plasma bubbles are regions of depleted plasma density generated in the post-sunset equatorial region of the ionosphere. Bubbles significantly affect total electron count (TEC) and consequently alter communication and navigation capabilities. Here, the Global Assimilation of Ionospheric Measurements Gauss-Markov (GAIM-GM) model is studied in order to assess its capability to accurately model equatorial plasma bubbles. GAIM-GM uses the Ionospheric Forecast Model (IFM) as a background state modified through the application of a Kalman Filter to incorporate ionospheric observations such as Global Positioning System (GPS) total electron content (TEC) values. GPS TEC values representative of plasma bubble conditions are modeled and input into GAIM-GM along with a background IFM state and compared with GAIM-GM model runs with plasma bubbles absent. The model resolution, bubble depletion factor, filter time constant, and geophysical conditions are varied to assess model response. GAIM-GM is unable to reliably model plasma bubble magnitude and spatial extent due to several characteristics of the model and filter. The resolution of GAIM-GM, in both regional and global modes, is insufficient to capture the small scale of bubbles. Additionally, the sun synchronous movement of perturbations and lower bound of the Kalman filter affect the location and magnitude of depletion regions in the model.